Linear Inequalities and Absolute Value Flashcards

Grade 10 · Math · Flashcards

Key rules and concepts for solving inequalities and absolute value problems.

Flashcards

Linear inequality: Like a linear equation but uses <, >, ≤, or ≥ instead of =
Flip rule: Multiply or divide by a negative number → reverse the inequality sign
Open circle (number line): Endpoint NOT included; used for strict inequalities < or >
Closed circle (number line): Endpoint IS included; used for ≤ or ≥
Compound inequality (AND): Both conditions true simultaneously; intersection; e.g., -3 < x < 7
Compound inequality (OR): Either condition can be true; union; e.g., x < -2 or x > 5
Absolute value |x|: Distance from zero on the number line; always non-negative
|x| = c (c > 0): x = c or x = -c; two solutions
|x| = c (c < 0): No solution — absolute value can't be negative
|x| < c (c > 0): -c < x < c; AND compound inequality (between)
|x| > c (c > 0): x < -c or x > c; OR compound inequality (outside)
Memory trick for absolute value inequalities: 'Less-AND, greatOR': < gives AND (between), > gives OR (outside)
Solution set of an inequality: All real numbers satisfying the inequality; often an interval on the number line